SIAM Journal on Control and Optimization, Volume 58, Issue 3, Page 1597-1625, January 2020.
In this paper we consider a Stokes system with Navier-slip boundary conditions. The main results concern the behavior of the cost of null controllability with respect to the diffusion coefficient when the control acts in the interior. In particular, we prove in $(0,\pi)^2$ that for a sufficiently large time the cost decays exponentially as the diffusion coefficient vanishes, whereas in $(0,\pi)^3$ we prove that for most of the control domains and for any time $T>0$ the cost explodes exponentially as the diffusion coefficient vanishes.

中文翻译：

---

运输项为零扩散极限的斯托克斯问题的一致可控性

SIAM控制与优化杂志，第58卷，第3期，第1597-1625页，2020
年1月。在本文中，我们考虑具有Navier滑移边界条件的Stokes系统。主要结果涉及当控件作用于内部时，零扩散系数相对于扩散系数的行为。特别是，我们在$（0，\ pi）^ 2 $中证明，在足够长的时间内，成本随着扩散系数的消失呈指数下降，而在$（0，\ pi）^ 3 $中，我们证明对于大多数控制域，并且在任何时候$ T> 0 $，随着扩散系数的消失，成本呈指数爆炸式增长。